Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups

Know about the book -

Algebraic $\overline {\mathbb {Q}}$-Groups as Abstract Groups is written by Olivier Frécon and published by American Mathematical Soc.. It's available with International Standard Book Number or ISBN identification 1470429233 (ISBN 10) and 9781470429232 (ISBN 13).

The author analyzes the abstract structure of algebraic groups over an algebraically closed field . For of characteristic zero and a given connected affine algebraic Q -group, the main theorem describes all the affine algebraic Q -groups such that the groups and are isomorphic as abstract groups. In the same time, it is shown that for any two connected algebraic Q -groups and , the elementary equivalence of the pure groups and implies that they are abstractly isomorphic. In the final section, the author applies his results to characterize the connected algebraic groups, all of whose abstract automorphisms are standard, when is either Q or of positive characteristic. In characteristic zero, a fairly general criterion is exhibited.